Jones (1969) in Historical Topics for the Mathematics Classroom, of the National Council of Teachers of Mathematics claims that History and up-to-date information about the development of mathematics could a a useful tool for the teacher who wishes to teach "why". Jone's "whys" are of three kinds: chronological, logical and pedagogical. Briefly, chronological whys are about looking at specific facts, (such as the fact that there are 360 degrees in a full turn) or more generally at definitions or axiomatic systems and their development. Logical whys serve into building an understanding of the structure of the axiomatic system through its development and not through its finalised form, which possibly contradicts the historical development as well as "the way perceptions grow in the minds of many of our students" (p.2). Pedagogical whys "are yhe processes and devices that are not dictated by well-established arbitrary definitions and do not have a logical uniqueness", where history may serve in helping the teacher identify a process during which students use a pedagogical sequence to guide their thoughts and finally achieve an in-depth understanding.
What is very interesting is the fact that Jones often implies that all these tools and pedagogical reccomendations can function in the hands of skillful teachers, who, in their turn have very clear purposes in using these tools and make a very detailed planning for their employment. The author ends up suggesting that "the ingenuity of the teacher" is one of the factors that will determine the approach that may be used. Moreover, knowing history on the behalf of the teacher, may help in clearly distinguishing between old mathematics, newer concepts and end up with an informed perspective on what "modern mathematics" is.
Taking into consideration the fact that, as Jones mentions, history should be an important component in teachers' education programs, I have come to think that before discussing about employing students' syllabuses based upon history (and culture), the first step shuld be to make sure that the teachers have a good understanding of what they teach, not just as a tool, but mainly as a human procedure that assists in moving the world forward. As the article begins with the words of Bazun, a maths teacher; "algebra is made repellent by the unwillingness or inability of teachers to explain why...", I come to think that he must have a large proportion of rightness in his sayings. Is the modern maths teacher in position to answer to questions such as "why didn't we divide the circle into 100 degrees in the first place?" Probably not. Students perhaps receive this inability and they are therefore lead to the dislike towards something that come to be meaningless in its gist, even for the person who is in charge to teach them that very discipline.